Can you analogize? I am having some difficulty understanding exactly the differences. I'm trying to learn, though.
Virtual Machines: WINE, VMWare
Virtual Machines operate by running the program on the computer (Host PC) and emulate services. So a Windows program will operate normally under WINE but its Windows calls will be handled by WINE instead of Windows.
Emulators: BOCHS, Virtual PC for Mac
Emulators emulate the PC. They don't run x86 instructions directly, rather they interpret them. So instead of simply calling the "add" instruction they would simulate the "add" instruction by creating 2 variables and add them in the program. This interpretation slows down the execution process significantly.
There are advances in some emulators that increase the speed, for example dynamic recompilation. This technique uses the executable (binary) as a "source code" of sorts and recompiles for the native processor and then executes the recompiled code. I believe Virtual PC works this way. This is also a popular way of emulating console gaming platforms to increase performance.
Virtual Machines can only work for applications that would work on the architecture natively. So a Windows program would run on a PC operating Linux but not a Mac since Macs use a completely different processor. In order to run non-native code you'd have to emulate.